Preheat the oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt.
In a large bowl, cream together the softened butter, brown sugar, and granulated sugar until light and fluffy.
Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the butter mixture, alternating with the sour cream, starting and ending with the flour mixture. Mix until just combined.
Fold in the diced peaches and cinnamon gently until evenly distributed.
Pour the batter into the prepared baking pan and spread it evenly. Sprinkle the tablespoon of sugar over the top.
Bake for 35-40 minutes, or until a toothpick inserted in the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes before transferring it to a wire rack to cool completely.